Like you suggest one way to do this sort of thing that the player is rewarded some way playing their flaws.... I'm still not a huge fan, I find such bribery unnecessary, but it is not offensive to me.
And here's where we get into the interaction of game mechanics and voluntary roleplaying.
Some players will never make a sub-optimal or dangerous choice. These are often the ones who view the game as a purely tactical exercise, with skirmishes connected by railroad tracks of narrative. But sometimes they're the ones for whom it's a power fantasy, in which their character must remain untouchable and invincible.
Some players will gleefully get into all kinds of trouble without any urging. The malevolent kind are those who protest "But that's what my character would do!" after some sort of chaos-monkey exploit which ruins the game for the entire party and requires ham-handed GM action to save the narrative. Other players are just theatrically engaged, and have a more healthy expectation of shared narrative with the other players.
And most folks probably lie on the middle of the spectrum. They see no reason to gratuitously make a choice that might negatively impact their PC's health, success, or reputation. But, in return for a small in-game recompense for their trouble, they might be willing to climb off a safe perch and allow a bit of grime on their narrative persona.
And that's only the player side of the issue, neglecting the frustrated-author narrative-railroading GM who already has the story plotted out in their head and are merely waiting to inflict it on their captive players. Which it sounds like we pretty much all agree is a generally bad idea.